script_ber_mimo_mmse_bpsk_rayleigh_channel.rar_BER_BER mimo_MIMO

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % All rights reserved by Krishna Pillai, http://www.dsplog.com % The file may not be re-distributed without explicit authorization % from Krishna Pillai. % Checked for proper operation with Octave Version 3.0.0 % Author : Krishna Pillai % Email : krishna@dsplog.com % Version : 1.0 % Date : 02nd Novemeber 2008 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Script for computing the BER for BPSK modulation in a % Rayleigh fading channel with 2 Tx, 2Rx MIMO channel % Minimum Mean Square Error equalization clear N = 5000; % number of bits or symbols Eb_N0_dB = [0:25]; % multiple Eb/N0 values nTx = 2; nRx = 2; for ii = 1:length(Eb_N0_dB) % Transmitter ip = rand(1,N)>0.5; % generating 0,1 with equal probability s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0 sizes=size(s) sMod = kron(s,ones(nRx,1)); sizesMod= size(sMod)%2 864 sMod = reshape(sMod,[nRx,nTx,N/2]); % grouping in [nRx,nTx,N/NTx ] matrix sizesMod2= size(sMod) %2 2 864/2 h = 1/sqrt(2)*[randn(nRx,nTx,N/nTx) + j*randn(nRx,nTx,N/nTx)]; % Rayleigh channel n = 1/sqrt(2)*[randn(nRx,N/nTx) + j*randn(nRx,N/nTx)]; % white gaussian noise, 0dB variance % Channel and noise Noise addition y = squeeze(sum(h.*sMod,2)) + 10^(-Eb_N0_dB(ii)/20)*n; sizeh= size(h) %2 2 864/2 % Receiver % Forming the MMSE equalization matrix W = inv(H^H*H+sigma^2*I)*H^H % H^H*H is of dimension [nTx x nTx]. In this case [2 x 2] % Inverse of a [2x2] matrix [a b; c d] = 1/(ad-bc)[d -b;-c a] hCof = zeros(2,2,N/nTx) ; hCof(1,1,:) = sum(h(:,2,:).*conj(h(:,2,:)),1) + 10^(-Eb_N0_dB(ii)/10); % d term hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1) + 10^(-Eb_N0_dB(ii)/10); % a term hCof(2,1,:) = -sum(h(:,2,:).*conj(h(:,1,:)),1); % c term hCof(1,2,:) = -sum(h(:,1,:).*conj(h(:,2,:)),1); % b term hDen = ((hCof(1,1,:).*hCof(2,2,:)) - (hCof(1,2,:).*hCof(2,1,:))); % ad-bc term hDen = reshape(kron(reshape(hDen,1,N/nTx),ones(2,2)),2,2,N/nTx); % formatting for division hInv = hCof./hDen; % inv(H^H*H) hMod = reshape(conj(h),nRx,N); % H^H operation yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization yMod = sum(hMod.*yMod,1); % H^H * y yMod = kron(reshape(yMod,2,N/nTx),ones(1,2)); % formatting yHat = sum(reshape(hInv,2,N).*yMod,1); % inv(H^H*H)*H^H*y % receiver - hard decision decoding ipHat = real(yHat)>0; % counting the errors nErr(ii) = size(find([ip- ipHat]),2); end simBer = nErr/N; % simulated ber EbN0Lin = 10.^(Eb_N0_dB/10); theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5)); p = 1/2 - 1/2*(1+1./EbN0Lin).^(-1/2); theoryBerMRC_nRx2 = p.^2.*(1+2*(1-p)); close all figure semilogy(Eb_N0_dB,theoryBer_nRx1,'bp-','LineWidth',2); hold on semilogy(Eb_N0_dB,theoryBerMRC_nRx2,'kd-','LineWidth',2); semilogy(Eb_N0_dB,simBer,'mo-','LineWidth',2); axis([0 25 10^-5 0.5]) grid on legend('theory (nTx=2,nRx=2, ZF)', 'theory (nTx=1,nRx=2, MRC)', 'sim (nTx=2, nRx=2, MMSE)'); xlabel('Average Eb/No*,dB'); ylabel('Bit Error Rate'); title('BER for BPSK modulation with 2x2 MIMO and MMSE equalizer (Rayleigh channel)'); title('Constellation 16-QAM �mission '); scatterplot(s,16,0,'r*'); grid on; title('Constellation 16-QAM avec STO '); scatterplot(yHat,16,0,'r*'); grid on; title('Constellation 16-QAM avec CFO ')